A tourist in Ireland wants to visit seven different cities. If the route is randomly selected, what is the probability that the tourist will visit the cities in alphabetical order?
Think about it. only one in seven is first, only 1 in 6 is second, ...
Pr=(1/7)(1/6)....
1/5054
1/5040
To calculate the probability that the tourist will visit the cities in alphabetical order, we need to first determine the total number of possible routes and then find the number of routes where the cities are in alphabetical order.
The total number of possible routes can be calculated using the factorial function. Since there are seven cities to visit, the total number of possible routes is represented by 7!.
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040
Now we need to determine the number of routes where the cities are in alphabetical order. Since there are seven cities, only one specific order can be considered alphabetical. Therefore, there is only 1 route where the cities are in alphabetical order.
Now we can calculate the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 5,040
Therefore, the probability that the tourist will visit the cities in alphabetical order is 1/5,040, which is approximately 0.000198.